A friend and I did a quick hike up Mt Matthews, the tallest peak in the Rimitaka forest park. You can read the trip report here: http://mrgilbe2.blogspot.co.nz/2012/10/mukamuka-munter-lite-edition.html
That 2 1/4 hours would be all uphill. Note to hikers new to New Zealand: When the Department of Conservation warns that the hike is steep - it is steep.